Ordered set

Wikipedia, the free encyclopedia - Cite This Source

Ordered set is used with distinct meanings in order theory.

• A set with a binary relation R on its elements that is reflexive (for all a in the set, aRa), antisymmetric (if aRb and bRa, then a=b) and transitive (if aRb and bRc, then aRc) is described as a partially ordered set or poset.
• If the binary relation is antisymmetric, transitive and also total (for all a and b in the set, aRb or bRa) then the set is a totally ordered set.
• If every non-empty subset has a least element then the set is a well-ordered set.

Wikipedia, the free encyclopedia © 2001-2006 Wikipedia contributors (Disclaimer)
This article is licensed under the GNU Free Documentation License.
Last updated on Wednesday September 19, 2007 at 07:04:28 PDT (GMT -0700)
View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation